Out of their respective monthly salaries, Soma spends `7/8` and Tina spends `4/5` on various expenses. The salary remaining with Tina after the expenses is Rs2000 more than that of Soma. If Tina’s monthly salary is Rs 4000 more than that of Soma, then what is Soma’s monthly salary?

Options

A. Rs 18000
B. Rs 24000
C. Rs 32000
D. Rs 16000

Answer

To solve the problem step by step, let's denote Soma's monthly salary as \( S \) and Tina's monthly salary as \( T \).

### Step 1: Set up the equations based on the problem statement.
1. **Soma's expenditure**: Soma spends \( \frac{7}{8} \) of his salary, so his remaining salary is:
\[ S - \frac{7}{8}S = \frac{1}{8}S \]

2. **Tina's expenditure**: Tina spends \( \frac{4}{5} \) of her salary, so her remaining salary is:
\[ T - \frac{4}{5}T = \frac{1}{5}T \]

### Step 2: Formulate the relationships given in the problem.
1. It is given that Tina's remaining salary is Rs 2000 more than Soma's remaining salary:
\[ \frac{1}{5}T = \frac{1}{8}S + 2000 \quad \text{(Equation 1)} \]

2. It is also given that Tina's salary is Rs 4000 more than Soma's salary:
\[ T = S + 4000 \quad \text{(Equation 2)} \]

### Step 3: Substitute Equation 2 into Equation 1.
Substituting \( T = S + 4000 \) into Equation 1:
\[ \frac{1}{5}(S + 4000) = \frac{1}{8}S + 2000 \]

### Step 4: Clear the fractions by multiplying through by the least common multiple (LCM).
The LCM of 5 and 8 is 40. Multiply the entire equation by 40:
\[ 40 \cdot \frac{1}{5}(S + 4000) = 40 \cdot \frac{1}{8}S + 40 \cdot 2000 \]
This simplifies to:
\[ 8(S + 4000) = 5S + 80000 \]

### Step 5: Distribute and simplify the equation.
Distributing on the left side:
\[ 8S + 32000 = 5S + 80000 \]

### Step 6: Rearrange the equation to isolate \( S \).
Subtract \( 5S \) from both sides:
\[ 8S - 5S + 32000 = 80000 \]
This simplifies to:
\[ 3S + 32000 = 80000 \]
Now, subtract 32000 from both sides:
\[ 3S = 80000 - 32000 \]
\[ 3S = 48000 \]

### Step 7: Solve for \( S \).
Divide both sides by 3:
\[ S = \frac{48000}{3} = 16000 \]

### Conclusion
Soma's monthly salary is Rs 16,000.